As computational thinking (CT) becomes increasingly acknowledged as an important skill in education, self-directed learning (SDL) emerges as a key strategy for developing this capability. The advent of generative AI (GenAI) conversational agents has disrupted the landscape of SDL. However, many questions still arise about several user experience aspects of these agents. This paper focuses on two of these questions: personalization and long-term support. As such, the first part of this study explores the effectiveness of personalizing GenAI through prompt-tuning using a CT-based prompt for solving programming challenges. The second part focuses on identifying the strengths and weaknesses of a GenAI model in a semester-long programming project. Our findings indicate that while prompt-tuning could hinder ease of use and perceived learning assistance, it might lead to higher learning outcomes. Results from a thematic analysis also indicate that GenAI is useful for programming and debugging, but it presents challenges such as over-reliance and diminishing utility over time.